{
 "cells": [
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 两次随机数实验"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [],
   "source": [
    "arr = np.zeros((100, 100))\n",
    "\n",
    "for i in range(1, 101):\n",
    "    for j in range(1, 101):\n",
    "        p = (i + j) / 2\n",
    "        arr[i-1, j-1] = p"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "im = plt.imshow(arr)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1cc338c4d90>]"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "flat_arr = arr.reshape(-1)\n",
    "plist = np.zeros(100)\n",
    "\n",
    "for i in range (1, 101):\n",
    "    res = list(filter(lambda x: x <= i, flat_arr))\n",
    "    plist[i-1] = len(res) / (100 * 100)\n",
    "\n",
    "plt.plot(plist)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "它似乎被定义为上是两个均匀分布的随机变量之和的联合分布函数（？）\n",
    "\n",
    "闭包形式的解需要使用数学卷积的知识。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0 0.0%\n",
      "10 0.5499999999999999%\n",
      "20 2.1%\n",
      "30 4.65%\n",
      "40 8.200000000000001%\n",
      "50 12.75%\n",
      "60 18.3%\n",
      "70 24.85%\n",
      "80 32.4%\n",
      "90 40.949999999999996%\n"
     ]
    }
   ],
   "source": [
    "for i in range(0, 100, 10):\n",
    "    print(i, str(plist[i] * 100) + '%')"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.10.8"
  },
  "orig_nbformat": 4
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
